PiecewiseLinearEmpiricalDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.PiecewiseLinearEmpiricalDist

All Implemented Interfaces:

Distribution
```
public class PiecewiseLinearEmpiricalDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for a piecewise-linear approximation of the empirical distribution function, based on the observations X₍₁₎,..., X_(n) (sorted by increasing order), and defined as follows (e.g.,). The distribution function starts at X₍₁₎ and climbs linearly by 1/(n - 1) between any two successive observations. The density is

f (x) = 1/[(n - 1)(X_(i+1) - X_(i))] for X_(i) <= x < X_(i+1) and i = 1, 2,..., n - 1.
The distribution function is

F(x) = 0          for x < X₍₁₎,

F(x) = (i - 1)/(n - 1) + (x - X_(i))/[(n - 1)(X_(i+1) - X_(i))]          for X_(i) <= x < X_(i+1),

F(x) = 1          elsewhere,

whose inverse is

F^-1(u) = X_(i) + ((n - 1)u - i + 1)(X_(i+1) - X_(i))
for (i - 1)/(n - 1) <= u <= i/(n - 1) and i = 1,..., n - 1.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description
`PiecewiseLinearEmpiricalDist(double[] obs)` Constructs a new piecewise-linear distribution using all the observations stored in `obs`.
`PiecewiseLinearEmpiricalDist(java.io.Reader in)` Constructs a new empirical distribution using the observations read from the reader `in`.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`double`	`cdf(double x)` Returns the distribution function F(x).
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`double`	`getMean()` Returns the mean.
`int`	`getN()` Returns n, the number of observations.
`double`	`getObs(int i)` Returns the value of X_(i).
`double[]`	`getParams()` Return a table containing parameters of the current distribution.
`double`	`getSampleMean()` Returns the sample mean of the observations.
`double`	`getSampleStandardDeviation()` Returns the sample standard deviation of the observations.
`double`	`getSampleVariance()` Returns the sample variance of the observations.
`double`	`getStandardDeviation()` Returns the standard deviation.
`double`	`getVariance()` Returns the variance.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`java.lang.String`	`toString()` Returns a `String` containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - PiecewiseLinearEmpiricalDist
```
public PiecewiseLinearEmpiricalDist(double[] obs)
```
    Constructs a new piecewise-linear distribution using all the observations stored in obs. These observations are copied into an internal array and then sorted.
  - PiecewiseLinearEmpiricalDist
```
public PiecewiseLinearEmpiricalDist(java.io.Reader in)
                             throws java.io.IOException
```
    Constructs a new empirical distribution using the observations read from the reader in. This constructor will read the first double of each line in the stream. Any line that does not start with a +, -, or a decimal digit, is ignored. The file is read until its end. One must be careful about lines starting with a blank. This format is the same as in UNURAN.
    
    Throws:
    
    java.io.IOException
- Method Detail
  - density
```
public double density(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns f (x), the density evaluated at x.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    x - value at which the density is evaluated
    
    Returns:
    density function evaluated at x
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    Parameters:
    x - value at which the distribution function is evaluated
    
    Returns:
    distribution function evaluated at x
  - barF
```
public double barF(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
    
    Specified by:
    
    barF in interface Distribution
    
    Overrides:
    
    barF in class ContinuousDistribution
    
    Parameters:
    x - value at which the complementary distribution function is evaluated
    
    Returns:
    complementary distribution function evaluated at x
  - inverseF
```
public double inverseF(double u)
```
    Description copied from class: ContinuousDistribution
    
    Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].
    
    Specified by:
    
    inverseF in interface Distribution
    
    Overrides:
    
    inverseF in class ContinuousDistribution
    
    Parameters:
    u - value at which the inverse distribution function is evaluated
    
    Returns:
    the inverse distribution function evaluated at u
  - getMean
```
public double getMean()
```
    Description copied from class: ContinuousDistribution
    
    Returns the mean.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class ContinuousDistribution
    
    Returns:
    the mean
  - getVariance
```
public double getVariance()
```
    Description copied from class: ContinuousDistribution
    
    Returns the variance.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    the variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: ContinuousDistribution
    
    Returns the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class ContinuousDistribution
    
    Returns:
    the standard deviation
  - getN
```
public int getN()
```
    Returns n, the number of observations.
  - getObs
```
public double getObs(int i)
```
    Returns the value of X_(i).
  - getSampleMean
```
public double getSampleMean()
```
    Returns the sample mean of the observations.
  - getSampleVariance
```
public double getSampleVariance()
```
    Returns the sample variance of the observations.
  - getSampleStandardDeviation
```
public double getSampleStandardDeviation()
```
    Returns the sample standard deviation of the observations.
  - getParams
```
public double[] getParams()
```
    Return a table containing parameters of the current distribution.
  - toString
```
public java.lang.String toString()
```
    Returns a String containing information about the current distribution.
    
    Overrides:
    
    toString in class java.lang.Object

F(x) =	0	for x < X₍₁₎,
F(x) =	(i - 1)/(n - 1) + (x - X_(i))/[(n - 1)(X_(i+1) - X_(i))]	for X_(i) <= x < X_(i+1),
F(x) =	1	elsewhere,

Class PiecewiseLinearEmpiricalDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

PiecewiseLinearEmpiricalDist

PiecewiseLinearEmpiricalDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getN

getObs

getSampleMean

getSampleVariance

getSampleStandardDeviation

getParams

toString